Non-equilibrium Dynamics and Random Matrices | |

Topic: | Gap probabilities and applications to geometry and random topology |

Speaker: | Antonio Lerario |

Affiliation: | Purdue University |

Date: | Wednesday, October 30 |

Time/Room: | 4:30pm - 5:30pm/S-101 |

Video Link: | https://video.ias.edu/nedrm/2013/1030-AntonioLerario |

What is the volume of the set of singular symmetric matrices of norm one? What is the probability that a random plane misses this set? What is the expected "topology" of the intersection of random quadric hypersurfaces? In this talk I will combine classical techniques form algebraic topology ("spectral sequences") with ideas from Random Matrix Theory and show how these problems can be solved using a local analysis of the "gap probability" at zero (the probability that a random matrix has a gap in its spectrum close to zero). (This is a joint work with E. Lundberg.)